A Paraconsistent Higher Order Logic

Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to achieve there are many potential applications of paraconsistent logics in knowledge-based systems, logical semantics of natural language, etc. Higher order logics have the advantages of being expressive and with several automated theorem provers available. Also the type system can be helpful. We present a concise description of a paraconsistent higher order logic with countable infinite indeterminacy, where each basic formula can get its own indeterminate truth value (or as we prefer: truth code). The meaning of the logical operators is new and rather different from traditional many-valued logics as well as from logics based on bilattices. The adequacy of the logic is examined by a case study in the domain of medicine. Thus we try to build a bridge between the HOL and MVL communities. A sequent calculus is proposed based on recent work by Muskens.Comment: Originally in the proceedings of PCL 2002, editors Hendrik Decker, Joergen Villadsen, Toshiharu Waragai (http://floc02.diku.dk/PCL/). Correcte

PARENTAL PERCEPTIONS OF LEARNING LOSS DURING COVID-19 SCHOOL CLOSURES IN 2020

Schools across the UK were mostly closed from March to July 2020 due to Covid-19. Therefore, parents and children found themselves thrust into a prolonged period of home-schooling. In this study, parents (N = 2,122) reported on their children’s (N = 3,230) home-schooling experiences and its impacts on their children’s academic progress. Parental reports suggest that children spent around 3 hours each weekday doing schoolwork at home. Children enrolled in private secondary schools received 4 hours of virtual lessons each weekday from teachers, while state school children received just 1 hour. Parents, on the whole, reported concern for children’s academic progress. This is particularly so for children in secondary school and, most strikingly, those in school years antecedent to final exams (Years 10 and 12). Parents were less concerned about academic progress for those in Years 11 and 13, who had received their final exam grades shortly before the time of the survey. This study highlights the fact that children have been unequally affected by Covid-19 school closures, depending on their year group and school type, which should be considered in future research and policy

Weakening the glass ceiling: does organizational growth reduce gender segregation in the upper tiers of Danish local government?

The theory of representative bureaucracy highlights gender segregation in the public sector and its detrimental implications for public policy outcomes. Focusing attention on organisational responses to this protracted problem, we supply evidence on whether organizational growth provides potential for change in the upper echelons of the public sector. An evaluation of the relationship between new hires and gender representation within the management tiers of Danish local government reveals an association between the recruitment of additional employees and improved gender integration. This is particularly pronounced for public organizations that employ fewer women. Implications for theory and practice are discussed

Designing a generic, adaptive protocol resource for the measurement of health impact in cash transfer pilot and feasibility studies and trials in high-income countries

INTRODUCTION: In the context of the COVID-19 pandemic, upstream interventions that tackle social determinants of health inequalities have never been more important. Evaluations of upstream cash transfer trials have failed to capture comprehensively the impacts that such systems might have on population health through inadequate design of the interventions themselves and failure to implement consistent, thorough research measures that can be used in microsimulations to model long-term impact. In this article, we describe the process of developing a generic, adaptive protocol resource to address this issue and the challenges involved in that process. The resource is designed for use in high-income countries (HIC) but draws on examples from a UK context to illustrate means of development and deployment. The resource is capable of further adaptation for use in low- and middle-income countries (LMIC). It has particular application for trials of Universal Basic Income but can be adapted to those covering other kinds of cash transfer and welfare system changes. METHODS: We outline two types of prospective intervention based on pilots and trials currently under discussion. In developing the remainder of the resource, we establish six key principles, implement a modular approach based on types of measure and their prospective resource intensity, and source (validated where possible) measures and baseline data primarily from routine collection and large, longitudinal cohort studies. Through these measures, we seek to cover all areas of health impact identified in our theoretical model for use in pilot and feasibility studies. RESULTS: We find that, in general, self-reported measures alongside routinely collected linked respondent data may provide a feasible means of producing data capable of demonstrating comprehensive health impact. However, we also suggest that, where possible, physiological measures should be included to elucidate underlying biological effects that may not be accurately captured through self-reporting alone and can enable modelling of long-term health outcomes. In addition, accurate self-reported objective income data remains a challenge and requires further development and testing. A process of development and implementation of the resource in pilot and feasibility studies will support assessment of whether or not our proposed health outcome measures are acceptable, feasible and can be used with validity and reliability in the target population. DISCUSSION: We suggest that while Open Access evaluation instruments are available and usable to measure most constructs of interest, there remain some areas for which further development is necessary. This includes self-reported wellbeing measures that require paid licences but are used in a range of nationally important longitudinal studies instead of Open Access alternatives

Comparison theory and smooth minimal C*-dynamics

We prove that the C*-algebra of a minimal diffeomorphism satisfies Blackadar's Fundamental Comparability Property for positive elements. This leads to the classification, in terms of K-theory and traces, of the isomorphism classes of countably generated Hilbert modules over such algebras, and to a similar classification for the closures of unitary orbits of self-adjoint elements. We also obtain a structure theorem for the Cuntz semigroup in this setting, and prove a conjecture of Blackadar and Handelman: the lower semicontinuous dimension functions are weakly dense in the space of all dimension functions. These results continue to hold in the broader setting of unital simple ASH algebras with slow dimension growth and stable rank one. Our main tool is a sharp bound on the radius of comparison of a recursive subhomogeneous C*-algebra. This is also used to construct uncountably many non-Morita-equivalent simple separable amenable C*-algebras with the same K-theory and tracial state space, providing a C*-algebraic analogue of McDuff's uncountable family of II_1 factors. We prove in passing that the range of the radius of comparison is exhausted by simple C*-algebras.Comment: 30 pages, no figure

Contribution of income and job strain to the association between education and cardiovascular disease in 1.6 million Danish employees

AIMS: We examined the extent to which associations between education and cardiovascular disease (CVD) morbidity and mortality are attributable to income and work stress. METHODS AND RESULTS: We included all employed Danish residents aged 30-59 years in 2000. Cardiovascular disease morbidity analyses included 1 638 270 individuals, free of cardiometabolic disease (CVD or diabetes). Mortality analyses included 41 944 individuals with cardiometabolic disease. We assessed education and income annually from population registers and work stress, defined as job strain, with a job-exposure matrix. Outcomes were ascertained until 2014 from health registers and risk was estimated using Cox regression. During 10 957 399 (men) and 10 776 516 person-years (women), we identified 51 585 and 24 075 incident CVD cases, respectively. For men with low education, risk of CVD was 1.62 [95% confidence interval (CI) 1.58-1.66] before and 1.46 (95% CI 1.42-1.50) after adjustment for income and job strain (25% reduction). In women, estimates were 1.66 (95% CI 1.61-1.72) and 1.53 (95% CI 1.47-1.58) (21% reduction). Of individuals with cardiometabolic disease, 1736 men (362 234 person-years) and 341 women (179 402 person-years) died from CVD. Education predicted CVD mortality in both sexes. Estimates were reduced with 54% (men) and 33% (women) after adjustment for income and job strain. CONCLUSION: Low education predicted incident CVD in initially healthy individuals and CVD mortality in individuals with prevalent cardiometabolic disease. In men with cardiometabolic disease, income and job strain explained half of the higher CVD mortality in the low education group. In healthy men and in women regardless of cardiometabolic disease, these factors explained 21-33% of the higher CVD morbidity and mortality

Cell fate takes a slug in BRCA1-associated breast cancer

Understanding why BRCA1 mutation carriers have a predilection for developing clinically aggressive basal-like breast tumors could inform the development of targeted treatment or prevention strategies. Analysis of both mouse and human mammary epithelial cells has identified a role for BRCA1 in orchestrating differentiation. The ability to isolate discrete epithelial subpopulations from mammary tissue has recently directed attention to luminal progenitor cells - the descendants of mammary stem cells - as the likely 'cells-of-origin' in BRCA1-associated breast cancer. A new publication has confirmed the importance of aberrant luminal cells as key culprits and provided insights on how BRCA1 haploinsufficiency biases luminal cells toward a basal-like fate through aberrant expression of the transcription factor SLUG

Designing a generic, adaptive protocol resource for the measurement of health impact in cash transfer trials

IntroductionIn the context of the COVID-19 pandemic, upstream interventions that tackle social determinants of health inequalities have never been more important. Evaluations of upstream cash transfer trials have failed to capture comprehensively the impacts that such systems might have on population health through inadequate design of the interventions themselves and failure to implement consistent, thorough research measures that can be used in microsimulations to model long-term impact. In this article, we describe the process of developing a generic, adaptive protocol resource to address this issue and the challenges involved in that process.MethodsWe outline two types of prospective intervention based on trials currently under discussion. In developing the remainder of the resource, we establish six key principles, implement a modular approach based on types of measure and their prospective resource intensity, and source (validated where possible) measures and baseline data primarily from routine collection and large, longitudinal cohort studies. Through these measures, we seek to cover all areas of health impact identified in our theoretical model.ResultsWe find that, in general, self-reported measures alongside routinely collected linked respondent data may provide data capable of demonstrating comprehensive health impact. However, we also suggest that, where possible, physiological measures should be included to elucidate underlying biological effects that may not be accurately captured through self-reporting alone and can enable modelling of long-term health outcomes.DiscussionWe suggest that while Open Access evaluation instruments are available and usable to measure most constructs of interest, there remain some areas for which further development is necessary. This includes self-reported wellbeing measures that require paid licences but are used in a range of nationally important longitudinal studies instead of Open Access alternatives

Breast cancer incidence after the start of mammography screening in Denmark

Mammography screening may lead to overdiagnosis of asymptomatic breast cancers, that would otherwise not have given rise to clinical symptoms. This aspect was studied in three regional screening programmes in Denmark, which started in Copenhagen municipality, Fyn county, and Frederiksberg municipality in 1991, 1993, and 1994, respectively. In these regions, we compared time trends in incidence of invasive breast cancer with the rest of Denmark. Since the number of clinical mammograms was relatively low, it was reasonable to assume that the breast cancer incidence outside the three screening regions represented the incidence of a population with low-intensity opportunistic screening. In Copenhagen and Fyn, a prevalence peak in incidence was seen during the first invitation round. During the subsequent invitation rounds, the incidence dropped to a level in line with the incidence expected without screening. The pattern was different in the small municipality of Frederiksberg, where the sensitivity was low during the first invitation round. Inclusion of screen-detected ductal carcinoma in situ cases did not change these results. The experiences from Copenhagen and Fyn show that organised mammography screening can operate without overdiagnosis of breast cancer